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Fourier Coefficient


For a periodic function f of period T, its nth complex Fourier coefficient is

 c_n=1/Tint_a^(a+T)f(x)e^(-2piinx/T)dx.

The Fourier coefficients are the constants in the corresponding Fourier series expansion of f.

In the Wolfram Language, the complex Fourier coefficient is implemented as FourierCoefficient[expr, t, n]. For the real trigonometric form, the cosine and sine coefficients are implemented as FourierCosCoefficient[expr, t, n] and FourierSinCoefficient[expr, t, n], respectively.


See also

Fourier Cosine Series, Fourier Series, Fourier Sine Series, Fourier Transform

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Cite this as:

Weisstein, Eric W. "Fourier Coefficient." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FourierCoefficient.html

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